I am a direct descendant of Cyrus Gates, father of Elisha Herrick Gates married to Betsey Kingsley, mother of Phidelia Gates. Elisha and Betsey had four children: Phidelia, b. 1821, Salmon b. 1826,Don Carlos Gates b. 1824- 1892, he is my line. Horace b. 1826. Betsey died from an allergic reaction to a bee sting when she was 29 years old. Elisha married Louisa Alford in 1831 and had several more children. The Gates Family Cemetery in Castleton, Vermont has twelve Gates family members buried there, including Revolutionary War soldier, Cyrus Gates.
I do not have any indication that Phidelia was adopted, or of any Native American ancestry in our family line. I have inherited a tremendous amount of family genealogy which I am continuing to sort through and if I find anything different, I will post it. Hope this helps clear things up for you!